Advertisements
Advertisements
प्रश्न
Find the direction cosines and direction ratios for the following vector
`3hat"i" - 4hat"j" + 8hat"k"`
Advertisements
उत्तर
The direction ratios of the `3hat"i" - 4hat"j" + 8hat"k"` are (3, – 4, 8)
The direction cosines of the vector `3hat"i" - 4hat"j" + 8hat"k"` are
`3/sqrt(3^2 + (-4)^2 + 8^2),(-4)/sqrt(3^2 + (-4)^2 + 8^2), 8/sqrt(3^2 + (-4)^2 + 8^2)`
`3/sqrt(9 + 16 + 64), (-4)/sqrt(9 + 16 + 64), 8/sqrt(9 + 16 + 64)`
`(3/sqrt(89), (-4)/sqrt(89), 8/sqrt(89))`
Direction ratios = (3, – 4, 8)
Direction cosines = `(3/sqrt(89), (-4)/sqrt(89), 8/sqrt(89))`
APPEARS IN
संबंधित प्रश्न
Find the angle between the lines whose direction ratios are 4, –3, 5 and 3, 4, 5.
If a line has direction ratios 2, −1, −2, determine its direction cosines.
Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, −1) and (4, 3, −1).
If the coordinates of the points A, B, C, D are (1, 2, 3), (4, 5, 7), (−4, 3, −6) and (2, 9, 2), then find the angle between AB and CD.
A line makes an angle of 60° with each of X-axis and Y-axis. Find the acute angle made by the line with Z-axis.
Write the ratio in which the line segment joining (a, b, c) and (−a, −c, −b) is divided by the xy-plane.
Write direction cosines of a line parallel to z-axis.
If a unit vector `vec a` makes an angle \[\frac{\pi}{3} \text{ with } \hat{i} , \frac{\pi}{4} \text{ with } \hat{j}\] and an acute angle θ with \[\hat{ k} \] ,then find the value of θ.
Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the distance of a point P(a, b, c) from x-axis.
If a line makes angles 90°, 135°, 45° with the x, y and z axes respectively, find its direction cosines.
Find the direction cosines and direction ratios for the following vector
`hat"i" - hat"k"`
Find the direction cosines of the line passing through the points P(2, 3, 5) and Q(–1, 2, 4).
The line `vec"r" = 2hat"i" - 3hat"j" - hat"k" + lambda(hat"i" - hat"j" + 2hat"k")` lies in the plane `vec"r".(3hat"i" + hat"j" - hat"k") + 2` = 0.
If a line makes angles 90°, 135°, 45° with x, y and z-axis respectively then which of the following will be its direction cosine.
The d.c's of a line whose direction ratios are 2, 3, –6, are ______.
If two straight lines whose direction cosines are given by the relations l + m – n = 0, 3l2 + m2 + cnl = 0 are parallel, then the positive value of c is ______.
A line in the 3-dimensional space makes an angle θ `(0 < θ ≤ π/2)` with both the x and y axes. Then the set of all values of θ is the interval ______.
Equation of a line passing through point (1, 2, 3) and equally inclined to the coordinate axis, is ______.
